The Justice Department chastised the Ferguson, Mo., police department in two separate letters sent this week, as tensions continued to simmer in the community after the police shooting of an unarmed black man last month.

The letters address complaints from residents of the St. Louis suburb after the death of Michael Brown, an 18-year-old. His death last month sparked days of protests and a Justice Department investigation of the police department. In one letter, Civil Rights Division attorney Christy Lopez urges Police Chief...